Comparing Mixed Numbers and Improper Fractions

Students learn to compare mixed numbers by first comparing the whole numbers. For example, to compare 4 1/5 and 5 1/3, note that 4 < 5, so 4 1/5 < 5 1/3. Students learn to compare mixed numbers that have the same whole numbers by comparing the fractions. For example, to compare 3 2/5 and 3 1/5, note that 2/5 > 1/5, so 3 2/5 > 3 1/5. Students learn to compare improper fractions in the same way that they compare proper fractions. And students learn to compare a mixed number and an improper fraction by first changing the mixed number to an improper fraction, then comparing the improper fractions.